skip days

[Helios]

There may be a novel benefit of using the value

Mean month = 29 & 928 / 1749 days

This is that a concise value of the "skip day" and "skip cycle" can be given

S = 1 + 1 / [ ( M / 29 ) - 1 ] = 55 & 21 / 32 days
M = 29*[ 1 + 1 / ( S - 1 ) ] = 29 & 928 / 1749 days

For every 1781 days, there are 32 skip days, and

= 107 yerms
= 1749 months
= 928 skip cycles
= 51649 days


So it seems that a value for the moon's age, by a number: 1 - 29, can be assigned to all days except skip days. A day count with all of the skip days extracted would leave a lunar count by which ( LC + ?? )MOD( 29 ) would give the moon's age.

[Karl Palmen]

Dear Helios and Calendar People

Helios's skip days are phantom days, like St Tibbs Day of the Discordian
Calendar which is skipped by its 73-date seasons to provide a leap day.
Helios skips a day from lunar months of 29 dates. A skipped day is a
dateless day.

The number of these skip days in a lunar calendar cycle is equal to the
number of 30-day months. The 1749-month cycle has 928 30-day months and
29*1749+928=51649 days. 928 is divisible by 29 and hence the number of
days 51649 is also divisible by 29 and so we have a skip day cycle equal
the 1/29 of the lunar calendar cycle, which is 1781 days of which 32 are
skip days.

The average interval between skip days (including the skip day) is
1781/32 = 55 & 21/32 days (as reckoned by Helios).
This leads to intervals of 55,55,56 days with one interval of 55 days
omitted from every 11th cycle of 55,55,56.

I note that 39 1749-month cycles make a 5515-year lunisolar cycle with
mean month of 29.530589 days and mean year of 365.24225 days. This was
discovered by Helios.


An alternative to skipping a DAY once every 55 or 56 days in lunar
months of 29 un-skipped days, is to have lunar months of 30 dates and
skip (or sacrifice) a DATE once every 63 or 62 days. This gives rise to
a 703-month cycle of 692*30=20760 days.
This skip-date cycle is considerably simpler in structure than Helios's
skip-day cycle.

The number of skipped dates is equal to the number of 29-day months so
is 330. The lunar cycle has
43 yerms
703 months
330 skipped dates in 30 skip cycle with 11 skipped dates
20760 days
692 30-day cycles

I note that 118 lunar 703-month cycles make a 6707-year lunisolar cycle
with mean month of 29.530583 days and mean year of 365.24228 days.


One could do better, if one were to find a lunar cycle in
http://www.hermetic.ch/cal_stud/lunarcal/lunacycl.htm whose number of
days has a larger common divisor with the number of 30-day months (=
number of skip days) or the number of 29-day months (= number of skip
dates) than 29 or 30 respectively. However, such a cycle cannot be found
because the number of dates in that cycle would also have this common
divisor and this number of dates is merely 29 or 30 respectively times
the number of months, which has no common divisor with the number of
days. Hence no larger common divisor can be found.

-----Original Message-----
From: East Carolina University Calendar discussion List
[mailto:CALNDR-L@...] On Behalf Of Helios
Sent: 07 September 2009 08:37
To: CALNDR-L@...
Subject: skip days

There may be a novel benefit of using the value

Mean month = 29 & 928 / 1749 days

This is that a concise value of the "skip day" and "skip cycle" can be
given

S = 1 + 1 / [ ( M / 29 ) - 1 ] = 55 & 21 / 32 days
M = 29*[ 1 + 1 / ( S - 1 ) ] = 29 & 928 / 1749 days

For every 1781 days, there are 32 skip days, and

= 107 yerms
= 1749 months
= 928 skip cycles
= 51649 days

KARL SAYS: The above applies to the complete lunar cycle of
29*1781=51649 days.
The 928 is the number of skip days in 29 skip cycles each with 32 skip
days.
It also has 1781 29-day cycles.


So it seems that a value for the moon's age, by a number: 1 - 29, can be
assigned to all days except skip days. A day count with all of the skip
days
extracted would leave a lunar count by which ( LC + ?? )MOD( 29 ) would
give
the moon's age.

Karl

10(12(18

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